Quote:
I've never once seen a private business that has both a "no guns" sign and armed security.

Banks?

The bank at which I conduct my business does not have a "no guns" sign nor do they have obvious armed security. I do not frequent other banks so I cannot speak for them. The only place, outside of government buildings, I can think of that has both a "no guns" sign and armed security (uniformed city police to be specific) is the local hospital. The hospital, however, is a county hospital that accepts some public funding so I do not count it as a private business.